What is the difference between deep learning and shallow learning?
That article only mentions "shallow learning" in the title and it mentions "shallow" to refer to the fact that deep learning models are not really learning any "deep" concepts, where "deep" here means "philosophically deep". So, I think the title is just (fairly?) provocative.

Currently, in machine learning, the expression "shallow learning" isn't really standardized, as opposed to deep learning, which refers to learning, with gradient descent and back-propagation, from (typically) huge amounts of data with neural networks. Nevertheless, "shallow learning" may occasionally refer to everything that isn't deep learning (e.g. traditional machine learning models, such as support vector machines), but most likely it refers to learning in neural networks with only a small number (0-2) of hidden layers (i.e. non-deep neural networks). 

Note that the difference between deep and shallow neural networks isn't really clear. Some people may consider neural networks with only 1-2 hidden layers already deep, while others may consider only neural networks with e.g. 5-10 hidden layers deep. This also shows that deep learning isn't actually well-defined too.

The other linked article actually says


  CNN performance was compared to that of conventional (shallow) machine learning methods, including ridge regression (RR) on the images’ principal components and support vector regression.


So, in this article, they use "shallow learning" to refer to traditional (or conventional) machine learning models, which confirms what I said above.